It is well known from communication theory that the non-uniform use of a signal constellation may result in a “shaping” gain. This is due to the reduced average transmission power that results from less-frequent use of constellation points with high energy. The constellation signal may have a Gaussian distribution to achieve capacity in an Additive White Gaussian Noise Channel (AWGNC).
The benefits of a shaping gain are similar to those for a coding gain. For example, less transmitter power, which equates to a less expensive transmitter, is obtained with the same system performance (e.g., the data rate at a given signal-to-noise ratio (SNR)). Alternatively, greater system performance can be achieved for the same transmitter power.
Signal-processing systems that utilize shaping gain may be less complex than other signal processing methods, yet still achieve an incremental performance gain (e.g., about one decibel (dB)) without the need for more iterations by an iterative decoder or for a more powerful code.
Shaping gain has been used in voice-band modems, but only with trellis-coded modulation (TCM). Unfortunately, obtaining a shaping gain is not a straight-forward process in Digital Subscriber Line (DSL) systems using Low Density Parity Check (LDPC)-coded modulation (LCM).